D'Hondt method: Difference between revisions

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The '''d'Hondt method''' or the Jefferson method (both are equivalent, but described differently) is a highest averages method for allocating seats. This system favors large parties slightly more than the other popular [[divisor method]], [[Sainte-Laguë method|Sainte-Laguë]], does. The method described is named in the United States after Thomas Jefferson, who introduced the method for proportional allocation of seats in the United States House of Representatives in 1792, and in Europe after Belgian mathematician Victor D'Hondt, who described the methodology in 1878.
 
It is used in: Argentina, Austria, Bulgaria, Chile, Denmark (for local elections), Finland, Israel, the Netherlands, Poland, Portugal and Spain, as well as elections to the European Parliament in some countries. The method is named after Belgian mathematician [[Victor d'Hondt]]. Jefferson's method is named after Thomas Jefferson, and was used to apportion the U.S. House of Representatives between 1792 and 1840.
 
==Allocation==
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In some cases, a [[election threshold|threshold]] or ''barrage'' is set, and any list which does not receive that threshold will not have any seats allocated to it, even if it received enough votes to otherwise have been rewarded with a seat. Examples of countries using this threshold are Israel (1.5%) and Belgium (5%, on regional basis).
 
Some systems allow parties to associate their lists together into a single ''cartel'' in order to overcome the threshold, while some systems set a separate threshold for cartels. Smaller parties often form pre-election [[coalition]]scoalitions to make sure they get past the election threshold.
 
== Jefferson's method ==
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== Computational complexity ==
Let <math>s</math> be the number of seats and <math>r</math> be the number of parties. The standard sequential allocation procedure determines the outcome in <math>O(s \log r)</math> time. A moreMore sophisticated algorithmalgorithms can determine the outcome in <math>O(r \log r)</math> time.<ref name="Gall 2003 pp. 325–333">{{cite journal | last=Gall | first=Françoise Le | title=Determination of the modes of a Multinomial distribution | journal=Statistics & Probability Letters | publisher=Elsevier BV | volume=62 | issue=4 | year=2003 | issn=0167-7152 | doi=10.1016/s0167-7152(02)00430-3 | pages=332-333}}</ref><ref name="White Hendy 2010 pp. 63–68">{{cite journal | last=White | first=W.T.J. | last2=Hendy | first2=M.D. | title=A fast and simple algorithm for finding the modes of a multinomial distribution | journal=Statistics & Probability Letters | publisher=Elsevier BV | volume=80 | issue=1 | year=2010 | issn=0167-7152 | doi=10.1016/j.spl.2009.09.013 | pages=63–68}}</ref>
 
== Extensions of theory ==
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